Cannot type on input inside a popover inside a menu

# Bug report

## Current behavior

I simply cannot type inside an input that is placed inside a popover inside the menu, it looks like its losing focus after you hit the first key.

## Expected behavior

I should be able to interact with any element inside a menu.

## Reproducible example

https://codesandbox.io/p/sandbox/elastic-browser-s2dfsq

## Base UI version

`"@base-ui-components/react": "^1.0.0-beta.3",`

## Which browser are you using?

Chrome

## Which OS are you using?

Mac OS